Introduction to Risk Management

1. Introduction to Risk Management Risk Management Prof. Ali Nejadmalayeri, a.k.a. “Dr N”

2. Origin of Risk Management • Mankind has always fear forces of nature and attempted to be in their “good” side • Natural deities sun, moon, water, etc. were thought of controlling entities of these forces • As man evolved, so did his methods of harnessing and controlling nature • Probability and statistics invented to deal with gambling and actuarial challenges • Modern financial theories and instruments are latest inventions to deal with risk! • Must read: Against the Gods: The Remarkable Story of Risk By Peter L. Bernstein

3. Basic Concepts • Imagine you want to make a car noise-free. What would you do? • Find out what “the noise” looks like • Design a wave with exact shape but opposite cycles to cancel the noise • Walla! You have a noise-free car! • Now imagine fluctuations in wealth, cash flows, values, prices, etc. How can you make them less volatile? Any ideas?

4. Heuristically Speaking Imagine the fluctuations in value looks like this Original Wave

5. Heuristically Speaking Original Wave Now imagine that is financial instrument which its fluctuations in value looks like this, so if we add this instrument to the mix Canceling Wave

6. Heuristically Speaking Resulting Wave Original Wave Then the resulting fluctuations should be a average of the two, much less volatile Canceling Wave

7. Risk Management 101 • Indentify the nature of risk • Price risk or quantity risk • For quantity risk, design insurance • For price risk, represent risk using: • Fluctuations of value, cash flows, etc. • Payoff of contractual agreements • Indentify the building blocks • Replicate the payoffs and fluctuations using other financial instruments • Construct a derivative with payoff replica

8. Quantity Risk • Early insurance companies like Lloyds of London wanted to offer a solution to an age-old problem: • If my shipments got lost in the high seas, how can my shipping business still survive? • Without insurance, pretty much no way! • Insurance, however, guarantees compensation of replacement cost for goods lost; solving quantity risk

9. Price Risk • Even if you still own 100% of goods, there’s no guarantee that value of these goods would stay same over time • Unless someone or something pays for losses of value due to natural fluctuation, you ought to live with risk • What if someone is willing to offer an “offsetting” payoff, maybe because they disagree with you on what is most likely next price movement? • Imagine you’re corn farmer and fear price of corn may drop drastically by the harvest time. What if another person thinks it would actually go up by then? You could strike a deal to sell him the corn!

10. Forward & Futures • In ancient India and Mesopotamia, farmers presold their crop for a price to speculators and merchants who were willing to take risk. These are known as forward contracts. • In late 18th century, Chicago merchants offered “standardized” forward contracts for agricultural products. These are futures. • Today there multiple futures markets around the globe. To name a few, CME, CBOT, ICE, NYMEX, etc. Offerings ranges from wheat and corn to T-bills and Fed Fund to Weather!

11. Futures • Contract to deliver pre-specified assets (commodities, financials, etc.) at a certain date at a pre-agreed price • Underlying asset are well defined • Maturity is well known in advance • Futures price is set at the beginning • No cash exchange initially • Initial and maintenance margins are required • Profit and losses are settled daily • positions are “Marked to Market”

12. Futures Payoff • Imagine you manage an index fund and want to protect the value for the next year. You are long in the index, so wherever index goes, you go the same way: Fund Payoff Future Portfolio Value Future Index Value Current Value

13. Futures Payoff • Now if you sell some futures contracts, let’s see what happens. When your portfolio value drops, the buyer needs to bring pre-agreed value, current value of the index. So you cover the difference! Fund Payoff Gains from Futures Position Future Portfolio Value Future Index Value Losses Future Payoff Current Value

14. Derivatives • Forward and futures are examples of derivatives; instruments that derive their value from some primitive like commodities, stocks, bonds, etc. • Major derivatives are: • Forward and Futures • Options • Swaps and Swaptions • Compound and Exotic Options • More advanced derivatives

15. Options • Bets on directional moves, up or down • Romans and Phoenicians traded options • Tulip mania in Holland was frothed with options, mostly “call” or right to buy • Early American options were called “privileges” and come under scrutiny after Great Crash of 1929 • In 1973 two financial economists, Fischer Black and Myron Scholes devised a formula for pricing options. Shortly after CBOE was born. • Today CBOE and other regional option markets handle multi million dollar transaction of a variety of sorts.

16. Option Payoff • Imagine again you manage an index fund and want to protect the value for the next year. You are long in the index, so wherever index goes, you go the same way: Fund Payoff Future Portfolio Value Future Index Value Current Value

17. Option Payoff • Now if you buy some put options, let’s see what happens. When your portfolio value drops, the put pays the strike price, say current value of the index. So you cover the difference again minus initial cost, of course! Fund Payoff Gains from Option Position Future Portfolio Value Future Index Value Put Option Payoff Losses Current Value

18. Hedging • The process of eliminating or reducing the net impact of price fluctuation is called “hedging”. • Similar to “hedging” you bets so your losses are not devastatingly large! • A “perfect hedge” removes all volatilities! • Difficult and very expensive to implement • A practical hedge then can be an alternative. This is an attempt to reduce major swings while tolerating some fluctuation.

19. Hedge & Hedge Ratio • Steps toward a hedge: • Understanding distribution of value/cash flow • Defining tolerable level of short fall • Measure probability of short fall • Evaluating impact of derivatives • Evaluating what kind of contract is available • Measuring what kind of position needed • Determining how many contracts are needed • This is the Hedge Ratio, i.e., the number of contracts needed for every share (unit) of the underlying asset